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作者：Geiges, Hansjoerg; Roettgen, Nena; Zehmisch, Kai
作者单位：University of Cologne; University of Freiburg
摘要：We construct a contact form on , , equal to the standard contact form outside a compact set and defining the standard contact structure on all of , which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a question posed by Helmut Hofer.
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作者：Mironov, Andrey E.
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics; Lomonosov Moscow State University
摘要：In this paper we study self-adjoint commuting ordinary differential operators of rank two. We find sufficient conditions when an operator of fourth order commuting with an operator of order 4g+2 is self-adjoint. We introduce an equation on potentials V(x),W(x) of the self-adjoint operator and some additional data. With the help of this equation we find the first example of commuting differential operators of rank two corresponding to a spectral curve of higher genus. These operators have polyn...
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作者：Bloch, Spencer; Esnault, Helene; Kerz, Moritz
作者单位：Free University of Berlin; University of Regensburg
摘要：We study the p-adic deformation properties of algebraic cycle classes modulo rational equivalence. We show that the crystalline Chern character of a vector bundle on the closed fibre lies in a certain part of the Hodge filtration if and only if, rationally, the class of the vector bundle lifts to a formal pro-class in K-theory on the p-adic scheme.
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作者：Gupta, Neena
作者单位：Tata Institute of Fundamental Research (TIFR)
摘要：We show that the Cancellation Conjecture does not hold for the affine space A(k)(3) over any field k of positive characteristic. We prove that an example of T. Asanuma provides a three-dimensional k-algebra A for which A is not isomorphic to k[X (1), X (2), X (3)] although A[T] is isomorphic to k[X (1), X (2), X (3), X (4)].
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作者：Chiodo, Alessandro; Eisenbud, David; Farkas, Gavril; Schreyer, Frank-Olaf
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of California System; University of California Berkeley; Humboldt University of Berlin; Saarland University
摘要：We formulate, and in some cases prove, three statements concerning the purity or, more generally, the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of a in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space of twisted level a curves of genus g and us...
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作者：Eichmair, Michael; Metzger, Jan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Potsdam
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作者：Mendel, Manor; Naor, Assaf
作者单位：Open University Israel; New York University; Microsoft; University of Washington; University of Washington Seattle
摘要：It is shown that for every epsilon a(0,1), every compact metric space (X,d) has a compact subset SaS dagger X that embeds into an ultrametric space with distortion O(1/epsilon), and dim(H) (S) >= (1 - epsilon) dim(H) (X), where dim (H) (.) denotes Hausdorff dimension. The above O(1/epsilon) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.
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作者：White, Brian
作者单位：Stanford University
摘要：Consider the mean curvature flow of an (n+1)-dimensional compact, mean convex region in Euclidean space (or, if n < 7, in a Riemannian manifold). We prove that elements of the mth homotopy group of the complementary region can die only if there is a shrinking S (k) xR (n-k) singularity for some ka parts per thousand currency signm. We also prove that for each m with 1a parts per thousand currency signma parts per thousand currency signn, there is a nonempty open set of compact, mean convex reg...
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作者：Kobayashi, Shinichi
作者单位：Tohoku University
摘要：Let p be a prime number and let E be an elliptic curve defined over ae of conductor N. Let K be an imaginary quadratic field with discriminant prime to pN such that all prime factors of N split in K. B. Perrin-Riou established the p-adic Gross-Zagier formula that relates the first derivative of the p-adic L-function of E over K to the p-adic height of the Heegner point for K when E has good ordinary reduction at p. In this article, we prove the p-adic Gross-Zagier formula of E for the cyclotom...
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作者：Gaitsgory, Dennis
作者单位：Harvard University
摘要：We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space of G-bundles on X is uniformized by the appropriate rational version of the affine Grassmannian, where the uniformizing map has contractible fibers.
